Math Textbook Recommendations
Preschool (Arithmetic) Feel free to skip Preschool if you can add and multiply with any amount of proficiency. Quick Arithmetic by Robert Carman * All the Math You'll Ever Need: A Self-Teaching Guide by Slavin (All the *Arithmetic* you'll ever need) * Speed Mathematics Simplified (Dover Books) by Edward Stoddard * Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks by Benjamin * The Mental Calculator's Handbook by Fountain and Koningsveld (More depth than the above, basic to intermediate level) * Dead Reckoning: Calculating Without Instruments by Doerfler (Warning: More advanced than the above, covers logarithms and trigonometric functions and their inverses, may require some calculus knowledge for maximum enjoyment)[[http://www.myreckonings.com/Dead_Reckoning/Dead_Reckoning.htm site]] Grade School *Algebra by Gelfand and Shen *Functions and Graphs by Gelfand, Glagoleva, and Shnol *The Method of Coordinates by Gelfand, Glagoleva, and Kirillov * Trigonometry by Gelfand and Saul * Kiselev's Geometry: Book I. Planimetry & Book II. Stereometry *Basic Mathematics by Lang and/or Precalculus with Unit Circle Trigonometry by Cohen High School *Euclid's Elements *Geometry Revisited by Coxeter * Elementary Calculus: An Infinitesimal Approach by H. Jerome Keislerhttps://www.math.wisc.edu/~keisler/calc.html *Calculus Vol I & II by Apostol or Calculus by Spivak *Linear Algebra and Its Applications by Strang *Ordinary Differential Equations by Tenenbaum and Pollard *A Primer of Abstract Mathematics by Ash *Conjecture and Proof by Laczkovich * Proofs from THE BOOK by Aigner and Ziegler University *Elements of Set Theory by Enderton *A Mathematical Introduction to Logic by Enderton *Generatingfunctionology by Wilfhttp://www.math.upenn.edu/~wilf/DownldGF.html *Linear Algebra by Shilov * Geometry by Brannan *Complex Analysis by Bak * Visual Complex Analysis by Needham *Probability and Random Processes by Grimmett & Stirzaker *Applied Partial Differential Equations by Haberman *Partial Differential Equations by Strauss *Numerical Analysis by Burden * Matrix Computations by Golub and Van Loan *Algebra by Artin *Topics in Algebra by Herstein * The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by Steele * Inequalities by Hardy, Littlewood, and Polya *Topology by Munkreshttp://www.math.toronto.edu/drorbn/classes/0405/Topology/etc/MunkresErrata.html and Counterexamples in Topology by Steen & Seebach *Principles of Mathematical Analysis by Rudinhttp://www.jirka.org/rudin-errata.html *Counterexamples in Analysis by Gelbaum and Olmsted * A Course of Modern Analysis by Whittaker and Watson and Special Functions by Wang and Guo * An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomeryhttp://www-personal.umich.edu/~hlm/nzm/ *Differential Geometry of Curves and Surfaces by Do Carmohttp://www.math.umn.edu/~tlawson/5378/docarmo_errata.pdf * Analysis on Manifolds by Munkres *Ordinary Differential Equations by Arnold *Algebraic Topology by Hatcherhttp://www.math.cornell.edu/~hatcher/AT/ATpage.html *Fourier Analysis; Complex Analysis; Real Analysis: Measure Theory, Integration, and Hilbert Spaces; Functional Analysis by Stein * Theoretical Numerical Analysis: A Functional Analysis Framework by Atkinson and Han *An Introduction to Probability Theory and Its Applications Vol. 1&2 by Feller *Partial Differential Equations by Jost *Basic Algebra I & II by Jacobson *Modern Graph Theory by Bollobás *A Classical Introduction to Modern Number Theory by Ireland and Rosen *Introduction to Analytic Number Theory by Apostol *Enumerative Combinatorics by Stanley Historical Light reading * e: the Story of a Number by Maor * Trigonometric Delights by Maor * MY BRAIN IS OPEN: The Mathematical Journeys of Paul Erdos by Schechter * A Mathematician Apology by Hardy * I Want to be a Mathematician: An Automathography by Halmos * The Apprenticeship of a Mathematician by Andre Weil * The Man Who Knew Infinity: A Life of the Genius Ramanujan by Kanigel * The Way I Remember It by Walter Rudin * The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860-1940 by Goodstein * Hilbert - Courant by Reid * The Honors Class: Hilbert's Problems and Their Solvers by Yandell * Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Ronan * Gauss: A Biographical Study by Bühler Textbooks and heavier works * A History of Mathematics by Katz * A History of Mathematics by Boyer and Merzbach * Mathematics and Its History by Stillwell * A History of Vector Analysis: The Evolution of the Idea of a Vectorial System by Crowe * Zermelo's Axiom of Choice: Its Origins, Development, and Influence (Dover Books) by Gregory H. Moore * A History of Algebraic and Differential Topology, 1900 - 1960 by Dieudonne * History of Topology by James * Emergence of the theory of Lie groups. An essay in the history of mathematics 1869 - 1926 by Hawkins * From Error Correcting Codes Through Sphere Packings to Simple Groups by Thompson * History of Banach spaces and Linear Operators by Pietch Original influential works, papers, and books of interest * A History of Greek Mathematics by Heath * The Works of Archimedes by Heath * Ptolemy's Almagest * On the Revolutions of Heavenly Spheres by Nicolaus Copernicus * The Principia: Mathematical Principles of Natural Philosophy by Isaac Newton, Cohen and Whitman (Translators) * Elements of Algebra by Leonhard Euler; notes added by Johann Bernoulli, and additions by Joseph-Louis Lagrange * Introductio in analysin infinitorum (Introduction to Analysis of the Infinite) by Leonhard Euler * Institutiones calculi differentialis (Foundations of Differential Calculus), Institutionum calculi integralis (Foundations of Integral Calculus) by Leonhard Euler * Disquisitiones Arithmeticae by Carl Gauss * An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole * The Mathematical Theory of Communication by Claude Shannon Errata Public Domain Material